Planets are massive celestial objects, so weighing them physically is practically impossible. It’s not like we have an Earth- or Jupiter-sized weighing scale just lying around. Therefore, the only way to do this is through a theoretical approach. Sounds a bit tough… how many of you knowledge-seekers would volunteer to undertake this cosmic mission?
This theoretical approach consists of physics (or that’s what scientists want us to think), and as it turns out, the approach is really simple. The answer lies almost completely in gravity.
The Scientific Approach
When you stand on a scale, the scale measures how strongly Earth’s gravity pulls on you, but how strongly the planet pulls depends not only on your weight, but also on the planet’s weight. The heavier the planet, the greater its gravitational pull, so scientists can weigh Earth by measuring how hard it pulls on another object.
First, let’s determine the mass of the Earth. Issac Newton’s Law of Universal Gravitation tells us that the force of attraction between two objects is proportional to the product of their masses divided by the square of the distance between their centers of mass. In order to simplify the calculation part, we assume that their geographical centers are their centers of mass (the point where the body’s maximum mass is present).
Since we know the radius of Earth, we can use Newton’s Law of Universal Gravitation to calculate the mass of Earth in terms of the gravitational force it has on an object, i.e., its weight on the Earth’s surface, using the radius of Earth as our distance variable.
Measuring the Mass
By observing the effect of a planet’s gravitational pull on an orbiting moon, the weight of the planet can be calculated. Now, the gravitational pull between the planet and the moon depends on the mass of the two bodies and the distance between them. The heavier the planet, the more gravitational pull there will be.
After the distance between the planet and the moon and the time it takes to complete one revolution is calculated, the weight of the planet can be calculated rather easily. Who knew that the seemingly impossible task of measuring something in outer space could be completed so simply with mathematics and physics?
- How Do We Weigh Planets? – NASA Space Place
- Scientific American
- How Do You Measure A Planet’s Mass? – Ask An Astronomers